Mathematics for FinanceMTP Nov 21Question 1334 of 512
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He effective rate of interest equivalent to the nominal rate of 7%\displaystyle 7\% converted monthly:

Options

A7.26%\displaystyle 7.26\%
B7.22%\displaystyle 7.22\%
C7.02%\displaystyle 7.02\%
D7.20%\displaystyle 7.20\%
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Correct Answer

✅ Option b — 7.22%\displaystyle 7.22\%

All Options:

  • A7.26%\displaystyle 7.26\%
  • B7.22%\displaystyle 7.22\%
  • C7.02%\displaystyle 7.02\%
  • D7.20%\displaystyle 7.20\%

Detailed Solution & Explanation

**Derivation of Effective Rate of Interest** Given: - Nominal interest rate (r\displaystyle r) = 7%\displaystyle 7\% per annum - Compounding Frequency = Converted monthly (m=12\displaystyle m = 12) **Step 1: Find the monthly interest rate (i\displaystyle i)** i=rm=7%12≈0.5833%=0.005833 per monthi = \frac{r}{m} = \frac{7\%}{12} \approx 0.5833\% = 0.005833 \text{ per month} **Step 2: Calculate the effective annual interest rate (E\displaystyle E)** E=(1+i)m−1E = (1 + i)^m - 1 E=(1+0.005833)12−1E = (1 + 0.005833)^{12} - 1 E=(1.005833)12−1E = (1.005833)^{12} - 1 E≈1.07229−1=0.07229 or 7.22%E \approx 1.07229 - 1 = 0.07229 \text{ or } 7.22\% Hence, **Option B** is the correct answer.

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